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  <div class="summary">
<a href="classEigen_1_1RealSchur-members.html">List of all members</a> &#124;
<a href="#pub-types">Public Types</a> &#124;
<a href="#pub-methods">Public Member Functions</a> &#124;
<a href="#pub-static-attribs">Static Public Attributes</a>  </div>
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<div class="title">Eigen::RealSchur&lt; MatrixType_ &gt; Class Template Reference<div class="ingroups"><a class="el" href="group__DenseLinearSolvers__chapter.html">Dense linear problems and decompositions</a> &raquo; <a class="el" href="group__DenseLinearSolvers__Reference.html">Reference</a> &raquo; <a class="el" href="group__Eigenvalues__Module.html">Eigenvalues module</a></div></div>  </div>
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<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
<div class="textblock"><h3>template&lt;typename MatrixType_&gt;<br />
class Eigen::RealSchur&lt; MatrixType_ &gt;</h3>

<p>Performs a real Schur decomposition of a square matrix. </p>
<p>This is defined in the Eigenvalues module.</p><div class="fragment"><div class="line"><span class="preprocessor">#include &lt;Eigen/Eigenvalues&gt;</span> </div>
</div><!-- fragment --><dl class="tparams"><dt>Template Parameters</dt><dd>
  <table class="tparams">
    <tr><td class="paramname">MatrixType_</td><td>the type of the matrix of which we are computing the real Schur decomposition; this is expected to be an instantiation of the <a class="el" href="classEigen_1_1Matrix.html" title="The matrix class, also used for vectors and row-vectors.">Matrix</a> class template.</td></tr>
  </table>
  </dd>
</dl>
<p>Given a real square matrix A, this class computes the real Schur decomposition: \( A = U T U^T \) where U is a real orthogonal matrix and T is a real quasi-triangular matrix. An orthogonal matrix is a matrix whose inverse is equal to its transpose, \( U^{-1} = U^T \). A quasi-triangular matrix is a block-triangular matrix whose diagonal consists of 1-by-1 blocks and 2-by-2 blocks with complex eigenvalues. The eigenvalues of the blocks on the diagonal of T are the same as the eigenvalues of the matrix A, and thus the real Schur decomposition is used in <a class="el" href="classEigen_1_1EigenSolver.html" title="Computes eigenvalues and eigenvectors of general matrices.">EigenSolver</a> to compute the eigendecomposition of a matrix.</p>
<p>Call the function <a class="el" href="classEigen_1_1RealSchur.html#aaf3b66df113d28a17e5213e93e8372db" title="Computes Schur decomposition of given matrix.">compute()</a> to compute the real Schur decomposition of a given matrix. Alternatively, you can use the RealSchur(const MatrixType&amp;, bool) constructor which computes the real Schur decomposition at construction time. Once the decomposition is computed, you can use the <a class="el" href="classEigen_1_1RealSchur.html#a1c9ed0b7109f58621557005c59ea6f99" title="Returns the orthogonal matrix in the Schur decomposition.">matrixU()</a> and <a class="el" href="classEigen_1_1RealSchur.html#a9f939aaf24a1fa73e9f69f7566500e69" title="Returns the quasi-triangular matrix in the Schur decomposition.">matrixT()</a> functions to retrieve the matrices U and T in the decomposition.</p>
<p>The documentation of RealSchur(const MatrixType&amp;, bool) contains an example of the typical use of this class.</p>
<dl class="section note"><dt>Note</dt><dd>The implementation is adapted from <a href="http://math.nist.gov/javanumerics/jama/">JAMA</a> (public domain). Their code is based on EISPACK.</dd></dl>
<dl class="section see"><dt>See also</dt><dd>class <a class="el" href="classEigen_1_1ComplexSchur.html" title="Performs a complex Schur decomposition of a real or complex square matrix.">ComplexSchur</a>, class <a class="el" href="classEigen_1_1EigenSolver.html" title="Computes eigenvalues and eigenvectors of general matrices.">EigenSolver</a>, class <a class="el" href="classEigen_1_1ComplexEigenSolver.html" title="Computes eigenvalues and eigenvectors of general complex matrices.">ComplexEigenSolver</a> </dd></dl>
</div><table class="memberdecls">
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Public Types</h2></td></tr>
<tr class="memitem:ad3a6ac65243d901525158f418c4d0582"><td class="memItemLeft" align="right" valign="top">typedef <a class="el" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Eigen::Index</a>&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1RealSchur.html#ad3a6ac65243d901525158f418c4d0582">Index</a></td></tr>
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Public Member Functions</h2></td></tr>
<tr class="memitem:aaf3b66df113d28a17e5213e93e8372db"><td class="memTemplParams" colspan="2">template&lt;typename InputType &gt; </td></tr>
<tr class="memitem:aaf3b66df113d28a17e5213e93e8372db"><td class="memTemplItemLeft" align="right" valign="top"><a class="el" href="classEigen_1_1RealSchur.html">RealSchur</a> &amp;&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="classEigen_1_1RealSchur.html#aaf3b66df113d28a17e5213e93e8372db">compute</a> (const <a class="el" href="structEigen_1_1EigenBase.html">EigenBase</a>&lt; InputType &gt; &amp;matrix, bool computeU=true)</td></tr>
<tr class="memdesc:aaf3b66df113d28a17e5213e93e8372db"><td class="mdescLeft">&#160;</td><td class="mdescRight">Computes Schur decomposition of given matrix.  <a href="classEigen_1_1RealSchur.html#aaf3b66df113d28a17e5213e93e8372db">More...</a><br /></td></tr>
<tr class="separator:aaf3b66df113d28a17e5213e93e8372db"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a23189e19e28e70d5d99e4a355370896b"><td class="memTemplParams" colspan="2">template&lt;typename HessMatrixType , typename OrthMatrixType &gt; </td></tr>
<tr class="memitem:a23189e19e28e70d5d99e4a355370896b"><td class="memTemplItemLeft" align="right" valign="top"><a class="el" href="classEigen_1_1RealSchur.html">RealSchur</a> &amp;&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="classEigen_1_1RealSchur.html#a23189e19e28e70d5d99e4a355370896b">computeFromHessenberg</a> (const HessMatrixType &amp;matrixH, const OrthMatrixType &amp;matrixQ, bool computeU)</td></tr>
<tr class="memdesc:a23189e19e28e70d5d99e4a355370896b"><td class="mdescLeft">&#160;</td><td class="mdescRight">Computes Schur decomposition of a Hessenberg matrix H = Z T Z^T.  <a href="classEigen_1_1RealSchur.html#a23189e19e28e70d5d99e4a355370896b">More...</a><br /></td></tr>
<tr class="separator:a23189e19e28e70d5d99e4a355370896b"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a57eea8f6a25be4ac710097fd6cce9366"><td class="memItemLeft" align="right" valign="top"><a id="a57eea8f6a25be4ac710097fd6cce9366"></a>
<a class="el" href="classEigen_1_1RealSchur.html#ad3a6ac65243d901525158f418c4d0582">Index</a>&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1RealSchur.html#a57eea8f6a25be4ac710097fd6cce9366">getMaxIterations</a> ()</td></tr>
<tr class="memdesc:a57eea8f6a25be4ac710097fd6cce9366"><td class="mdescLeft">&#160;</td><td class="mdescRight">Returns the maximum number of iterations. <br /></td></tr>
<tr class="separator:a57eea8f6a25be4ac710097fd6cce9366"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a2d89e0ee94baa7ebe226e68134cc36a2"><td class="memItemLeft" align="right" valign="top"><a class="el" href="group__enums.html#ga85fad7b87587764e5cf6b513a9e0ee5e">ComputationInfo</a>&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1RealSchur.html#a2d89e0ee94baa7ebe226e68134cc36a2">info</a> () const</td></tr>
<tr class="memdesc:a2d89e0ee94baa7ebe226e68134cc36a2"><td class="mdescLeft">&#160;</td><td class="mdescRight">Reports whether previous computation was successful.  <a href="classEigen_1_1RealSchur.html#a2d89e0ee94baa7ebe226e68134cc36a2">More...</a><br /></td></tr>
<tr class="separator:a2d89e0ee94baa7ebe226e68134cc36a2"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a9f939aaf24a1fa73e9f69f7566500e69"><td class="memItemLeft" align="right" valign="top">const MatrixType &amp;&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1RealSchur.html#a9f939aaf24a1fa73e9f69f7566500e69">matrixT</a> () const</td></tr>
<tr class="memdesc:a9f939aaf24a1fa73e9f69f7566500e69"><td class="mdescLeft">&#160;</td><td class="mdescRight">Returns the quasi-triangular matrix in the Schur decomposition.  <a href="classEigen_1_1RealSchur.html#a9f939aaf24a1fa73e9f69f7566500e69">More...</a><br /></td></tr>
<tr class="separator:a9f939aaf24a1fa73e9f69f7566500e69"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a1c9ed0b7109f58621557005c59ea6f99"><td class="memItemLeft" align="right" valign="top">const MatrixType &amp;&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1RealSchur.html#a1c9ed0b7109f58621557005c59ea6f99">matrixU</a> () const</td></tr>
<tr class="memdesc:a1c9ed0b7109f58621557005c59ea6f99"><td class="mdescLeft">&#160;</td><td class="mdescRight">Returns the orthogonal matrix in the Schur decomposition.  <a href="classEigen_1_1RealSchur.html#a1c9ed0b7109f58621557005c59ea6f99">More...</a><br /></td></tr>
<tr class="separator:a1c9ed0b7109f58621557005c59ea6f99"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a848ba492ee395686781a9edadbc8d2b7"><td class="memTemplParams" colspan="2">template&lt;typename InputType &gt; </td></tr>
<tr class="memitem:a848ba492ee395686781a9edadbc8d2b7"><td class="memTemplItemLeft" align="right" valign="top">&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="classEigen_1_1RealSchur.html#a848ba492ee395686781a9edadbc8d2b7">RealSchur</a> (const <a class="el" href="structEigen_1_1EigenBase.html">EigenBase</a>&lt; InputType &gt; &amp;matrix, bool computeU=true)</td></tr>
<tr class="memdesc:a848ba492ee395686781a9edadbc8d2b7"><td class="mdescLeft">&#160;</td><td class="mdescRight">Constructor; computes real Schur decomposition of given matrix.  <a href="classEigen_1_1RealSchur.html#a848ba492ee395686781a9edadbc8d2b7">More...</a><br /></td></tr>
<tr class="separator:a848ba492ee395686781a9edadbc8d2b7"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a733948e4b4ef5f09cf73dc6ccc7149c6"><td class="memItemLeft" align="right" valign="top">&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1RealSchur.html#a733948e4b4ef5f09cf73dc6ccc7149c6">RealSchur</a> (<a class="el" href="classEigen_1_1RealSchur.html#ad3a6ac65243d901525158f418c4d0582">Index</a> size=RowsAtCompileTime==<a class="el" href="namespaceEigen.html#ad81fa7195215a0ce30017dfac309f0b2">Dynamic</a> ? 1 :RowsAtCompileTime)</td></tr>
<tr class="memdesc:a733948e4b4ef5f09cf73dc6ccc7149c6"><td class="mdescLeft">&#160;</td><td class="mdescRight">Default constructor.  <a href="classEigen_1_1RealSchur.html#a733948e4b4ef5f09cf73dc6ccc7149c6">More...</a><br /></td></tr>
<tr class="separator:a733948e4b4ef5f09cf73dc6ccc7149c6"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a10f9307a8dc2259c86e6dba0edbde308"><td class="memItemLeft" align="right" valign="top"><a class="el" href="classEigen_1_1RealSchur.html">RealSchur</a> &amp;&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1RealSchur.html#a10f9307a8dc2259c86e6dba0edbde308">setMaxIterations</a> (<a class="el" href="classEigen_1_1RealSchur.html#ad3a6ac65243d901525158f418c4d0582">Index</a> maxIters)</td></tr>
<tr class="memdesc:a10f9307a8dc2259c86e6dba0edbde308"><td class="mdescLeft">&#160;</td><td class="mdescRight">Sets the maximum number of iterations allowed.  <a href="classEigen_1_1RealSchur.html#a10f9307a8dc2259c86e6dba0edbde308">More...</a><br /></td></tr>
<tr class="separator:a10f9307a8dc2259c86e6dba0edbde308"><td class="memSeparator" colspan="2">&#160;</td></tr>
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<tr class="heading"><td colspan="2"><h2 class="groupheader"><a name="pub-static-attribs"></a>
Static Public Attributes</h2></td></tr>
<tr class="memitem:a96deb686155894864c9e5539c732b194"><td class="memItemLeft" align="right" valign="top">static const int&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1RealSchur.html#a96deb686155894864c9e5539c732b194">m_maxIterationsPerRow</a></td></tr>
<tr class="memdesc:a96deb686155894864c9e5539c732b194"><td class="mdescLeft">&#160;</td><td class="mdescRight">Maximum number of iterations per row.  <a href="classEigen_1_1RealSchur.html#a96deb686155894864c9e5539c732b194">More...</a><br /></td></tr>
<tr class="separator:a96deb686155894864c9e5539c732b194"><td class="memSeparator" colspan="2">&#160;</td></tr>
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<h2 class="groupheader">Member Typedef Documentation</h2>
<a id="ad3a6ac65243d901525158f418c4d0582"></a>
<h2 class="memtitle"><span class="permalink"><a href="#ad3a6ac65243d901525158f418c4d0582">&#9670;&nbsp;</a></span>Index</h2>

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template&lt;typename MatrixType_ &gt; </div>
      <table class="memname">
        <tr>
          <td class="memname">typedef <a class="el" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Eigen::Index</a> <a class="el" href="classEigen_1_1RealSchur.html">Eigen::RealSchur</a>&lt; MatrixType_ &gt;::<a class="el" href="classEigen_1_1RealSchur.html#ad3a6ac65243d901525158f418c4d0582">Index</a></td>
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<dl class="deprecated"><dt><b><a class="el" href="deprecated.html#_deprecated000018">Deprecated:</a></b></dt><dd>since <a class="el" href="namespaceEigen.html" title="Namespace containing all symbols from the Eigen library.">Eigen</a> 3.3 </dd></dl>

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<h2 class="groupheader">Constructor &amp; Destructor Documentation</h2>
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<h2 class="memtitle"><span class="permalink"><a href="#a733948e4b4ef5f09cf73dc6ccc7149c6">&#9670;&nbsp;</a></span>RealSchur() <span class="overload">[1/2]</span></h2>

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template&lt;typename MatrixType_ &gt; </div>
<table class="mlabels">
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      <table class="memname">
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          <td class="memname"><a class="el" href="classEigen_1_1RealSchur.html">Eigen::RealSchur</a>&lt; MatrixType_ &gt;::<a class="el" href="classEigen_1_1RealSchur.html">RealSchur</a> </td>
          <td>(</td>
          <td class="paramtype"><a class="el" href="classEigen_1_1RealSchur.html#ad3a6ac65243d901525158f418c4d0582">Index</a>&#160;</td>
          <td class="paramname"><em>size</em> = <code>RowsAtCompileTime==<a class="el" href="namespaceEigen.html#ad81fa7195215a0ce30017dfac309f0b2">Dynamic</a>&#160;?&#160;1&#160;:&#160;RowsAtCompileTime</code></td><td>)</td>
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<span class="mlabels"><span class="mlabel">inline</span><span class="mlabel">explicit</span></span>  </td>
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<p>Default constructor. </p>
<dl class="params"><dt>Parameters</dt><dd>
  <table class="params">
    <tr><td class="paramdir">[in]</td><td class="paramname">size</td><td>Positive integer, size of the matrix whose Schur decomposition will be computed.</td></tr>
  </table>
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</dl>
<p>The default constructor is useful in cases in which the user intends to perform decompositions via <a class="el" href="classEigen_1_1RealSchur.html#aaf3b66df113d28a17e5213e93e8372db" title="Computes Schur decomposition of given matrix.">compute()</a>. The <code>size</code> parameter is only used as a hint. It is not an error to give a wrong <code>size</code>, but it may impair performance.</p>
<dl class="section see"><dt>See also</dt><dd><a class="el" href="classEigen_1_1RealSchur.html#aaf3b66df113d28a17e5213e93e8372db" title="Computes Schur decomposition of given matrix.">compute()</a> for an example. </dd></dl>

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<h2 class="memtitle"><span class="permalink"><a href="#a848ba492ee395686781a9edadbc8d2b7">&#9670;&nbsp;</a></span>RealSchur() <span class="overload">[2/2]</span></h2>

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template&lt;typename MatrixType_ &gt; </div>
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          <td class="memname"><a class="el" href="classEigen_1_1RealSchur.html">Eigen::RealSchur</a>&lt; MatrixType_ &gt;::<a class="el" href="classEigen_1_1RealSchur.html">RealSchur</a> </td>
          <td>(</td>
          <td class="paramtype">const <a class="el" href="structEigen_1_1EigenBase.html">EigenBase</a>&lt; InputType &gt; &amp;&#160;</td>
          <td class="paramname"><em>matrix</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">bool&#160;</td>
          <td class="paramname"><em>computeU</em> = <code>true</code>&#160;</td>
        </tr>
        <tr>
          <td></td>
          <td>)</td>
          <td></td><td></td>
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<p>Constructor; computes real Schur decomposition of given matrix. </p>
<dl class="params"><dt>Parameters</dt><dd>
  <table class="params">
    <tr><td class="paramdir">[in]</td><td class="paramname">matrix</td><td>Square matrix whose Schur decomposition is to be computed. </td></tr>
    <tr><td class="paramdir">[in]</td><td class="paramname">computeU</td><td>If true, both T and U are computed; if false, only T is computed.</td></tr>
  </table>
  </dd>
</dl>
<p>This constructor calls <a class="el" href="classEigen_1_1RealSchur.html#aaf3b66df113d28a17e5213e93e8372db" title="Computes Schur decomposition of given matrix.">compute()</a> to compute the Schur decomposition.</p>
<p>Example: </p><div class="fragment"><div class="line"><a class="code" href="group__matrixtypedefs.html#ga99b41a69f0bf64eadb63a97f357ab412">MatrixXd</a> A = <a class="code" href="classEigen_1_1DenseBase.html#ae814abb451b48ed872819192dc188c19">MatrixXd::Random</a>(6,6);</div>
<div class="line">cout &lt;&lt; <span class="stringliteral">&quot;Here is a random 6x6 matrix, A:&quot;</span> &lt;&lt; endl &lt;&lt; A &lt;&lt; endl &lt;&lt; endl;</div>
<div class="line"> </div>
<div class="line">RealSchur&lt;MatrixXd&gt; schur(A);</div>
<div class="line">cout &lt;&lt; <span class="stringliteral">&quot;The orthogonal matrix U is:&quot;</span> &lt;&lt; endl &lt;&lt; schur.matrixU() &lt;&lt; endl;</div>
<div class="line">cout &lt;&lt; <span class="stringliteral">&quot;The quasi-triangular matrix T is:&quot;</span> &lt;&lt; endl &lt;&lt; schur.matrixT() &lt;&lt; endl &lt;&lt; endl;</div>
<div class="line"> </div>
<div class="line"><a class="code" href="group__matrixtypedefs.html#ga99b41a69f0bf64eadb63a97f357ab412">MatrixXd</a> U = schur.matrixU();</div>
<div class="line"><a class="code" href="group__matrixtypedefs.html#ga99b41a69f0bf64eadb63a97f357ab412">MatrixXd</a> T = schur.matrixT();</div>
<div class="line">cout &lt;&lt; <span class="stringliteral">&quot;U * T * U^T = &quot;</span> &lt;&lt; endl &lt;&lt; U * T * U.transpose() &lt;&lt; endl;</div>
<div class="ttc" id="aclassEigen_1_1DenseBase_html_ae814abb451b48ed872819192dc188c19"><div class="ttname"><a href="classEigen_1_1DenseBase.html#ae814abb451b48ed872819192dc188c19">Eigen::DenseBase::Random</a></div><div class="ttdeci">static const RandomReturnType Random()</div><div class="ttdef"><b>Definition:</b> Random.h:114</div></div>
<div class="ttc" id="agroup__matrixtypedefs_html_ga99b41a69f0bf64eadb63a97f357ab412"><div class="ttname"><a href="group__matrixtypedefs.html#ga99b41a69f0bf64eadb63a97f357ab412">Eigen::MatrixXd</a></div><div class="ttdeci">Matrix&lt; double, Dynamic, Dynamic &gt; MatrixXd</div><div class="ttdoc">Dynamic×Dynamic matrix of type double.</div><div class="ttdef"><b>Definition:</b> Matrix.h:501</div></div>
</div><!-- fragment --><p> Output: </p><pre class="fragment">Here is a random 6x6 matrix, A:
   0.68   -0.33   -0.27  -0.717  -0.687  0.0259
 -0.211   0.536  0.0268   0.214  -0.198   0.678
  0.566  -0.444   0.904  -0.967   -0.74   0.225
  0.597   0.108   0.832  -0.514  -0.782  -0.408
  0.823 -0.0452   0.271  -0.726   0.998   0.275
 -0.605   0.258   0.435   0.608  -0.563  0.0486

The orthogonal matrix U is:
  0.348  -0.754 0.00435  -0.351  0.0146   0.432
  -0.16  -0.266  -0.747   0.457  -0.366  0.0571
  0.505  -0.157  0.0746   0.644   0.518  -0.177
  0.703   0.324  -0.409  -0.349  -0.187  -0.275
  0.296   0.372    0.24   0.324  -0.379   0.684
 -0.126   0.305   -0.46  -0.161   0.647   0.485
The quasi-triangular matrix T is:
   -0.2   -1.83   0.864   0.271    1.09   0.139
  0.647   0.298 -0.0536   0.676  -0.288  0.0231
      0       0   0.967  -0.201  -0.429   0.847
      0       0       0   0.353   0.603   0.694
      0       0       0       0   0.572   -1.03
      0       0       0       0  0.0184   0.664

U * T * U^T = 
   0.68   -0.33   -0.27  -0.717  -0.687  0.0259
 -0.211   0.536  0.0268   0.214  -0.198   0.678
  0.566  -0.444   0.904  -0.967   -0.74   0.225
  0.597   0.108   0.832  -0.514  -0.782  -0.408
  0.823 -0.0452   0.271  -0.726   0.998   0.275
 -0.605   0.258   0.435   0.608  -0.563  0.0486
</pre> 
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<h2 class="groupheader">Member Function Documentation</h2>
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<h2 class="memtitle"><span class="permalink"><a href="#aaf3b66df113d28a17e5213e93e8372db">&#9670;&nbsp;</a></span>compute()</h2>

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template&lt;typename MatrixType_ &gt; </div>
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template&lt;typename InputType &gt; </div>
      <table class="memname">
        <tr>
          <td class="memname"><a class="el" href="classEigen_1_1RealSchur.html">RealSchur</a>&amp; <a class="el" href="classEigen_1_1RealSchur.html">Eigen::RealSchur</a>&lt; MatrixType_ &gt;::compute </td>
          <td>(</td>
          <td class="paramtype">const <a class="el" href="structEigen_1_1EigenBase.html">EigenBase</a>&lt; InputType &gt; &amp;&#160;</td>
          <td class="paramname"><em>matrix</em>, </td>
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          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">bool&#160;</td>
          <td class="paramname"><em>computeU</em> = <code>true</code>&#160;</td>
        </tr>
        <tr>
          <td></td>
          <td>)</td>
          <td></td><td></td>
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<p>Computes Schur decomposition of given matrix. </p>
<dl class="params"><dt>Parameters</dt><dd>
  <table class="params">
    <tr><td class="paramdir">[in]</td><td class="paramname">matrix</td><td>Square matrix whose Schur decomposition is to be computed. </td></tr>
    <tr><td class="paramdir">[in]</td><td class="paramname">computeU</td><td>If true, both T and U are computed; if false, only T is computed. </td></tr>
  </table>
  </dd>
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<dl class="section return"><dt>Returns</dt><dd>Reference to <code>*this</code> </dd></dl>
<p>The Schur decomposition is computed by first reducing the matrix to Hessenberg form using the class <a class="el" href="classEigen_1_1HessenbergDecomposition.html" title="Reduces a square matrix to Hessenberg form by an orthogonal similarity transformation.">HessenbergDecomposition</a>. The Hessenberg matrix is then reduced to triangular form by performing Francis QR iterations with implicit double shift. The cost of computing the Schur decomposition depends on the number of iterations; as a rough guide, it may be taken to be \(25n^3\) flops if <em>computeU</em> is true and \(10n^3\) flops if <em>computeU</em> is false.</p>
<p>Example: </p><div class="fragment"><div class="line"><a class="code" href="group__matrixtypedefs.html#ga731599f782380312960376c43450eb48">MatrixXf</a> A = <a class="code" href="classEigen_1_1DenseBase.html#ae814abb451b48ed872819192dc188c19">MatrixXf::Random</a>(4,4);</div>
<div class="line">RealSchur&lt;MatrixXf&gt; schur(4);</div>
<div class="line">schur.compute(A, <span class="comment">/* computeU = */</span> <span class="keyword">false</span>);</div>
<div class="line">cout &lt;&lt; <span class="stringliteral">&quot;The matrix T in the decomposition of A is:&quot;</span> &lt;&lt; endl &lt;&lt; schur.matrixT() &lt;&lt; endl;</div>
<div class="line">schur.compute(A.inverse(), <span class="comment">/* computeU = */</span> <span class="keyword">false</span>);</div>
<div class="line">cout &lt;&lt; <span class="stringliteral">&quot;The matrix T in the decomposition of A^(-1) is:&quot;</span> &lt;&lt; endl &lt;&lt; schur.matrixT() &lt;&lt; endl;</div>
<div class="ttc" id="agroup__matrixtypedefs_html_ga731599f782380312960376c43450eb48"><div class="ttname"><a href="group__matrixtypedefs.html#ga731599f782380312960376c43450eb48">Eigen::MatrixXf</a></div><div class="ttdeci">Matrix&lt; float, Dynamic, Dynamic &gt; MatrixXf</div><div class="ttdoc">Dynamic×Dynamic matrix of type float.</div><div class="ttdef"><b>Definition:</b> Matrix.h:500</div></div>
</div><!-- fragment --><p> Output: </p><pre class="fragment">The matrix T in the decomposition of A is:
 0.523 -0.698  0.148  0.742
 0.475  0.986 -0.793  0.721
     0      0  -0.28  -0.77
     0      0 0.0145 -0.367
The matrix T in the decomposition of A^(-1) is:
-3.06 -4.57 -5.97  5.48
0.168 -2.62 -3.27   3.9
    0     0 0.427 0.573
    0     0 -1.05  1.35
</pre><dl class="section see"><dt>See also</dt><dd>compute(const MatrixType&amp;, bool, Index) </dd></dl>

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<h2 class="memtitle"><span class="permalink"><a href="#a23189e19e28e70d5d99e4a355370896b">&#9670;&nbsp;</a></span>computeFromHessenberg()</h2>

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template&lt;typename MatrixType_ &gt; </div>
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template&lt;typename HessMatrixType , typename OrthMatrixType &gt; </div>
      <table class="memname">
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          <td class="memname"><a class="el" href="classEigen_1_1RealSchur.html">RealSchur</a>&amp; <a class="el" href="classEigen_1_1RealSchur.html">Eigen::RealSchur</a>&lt; MatrixType_ &gt;::computeFromHessenberg </td>
          <td>(</td>
          <td class="paramtype">const HessMatrixType &amp;&#160;</td>
          <td class="paramname"><em>matrixH</em>, </td>
        </tr>
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          <td class="paramtype">const OrthMatrixType &amp;&#160;</td>
          <td class="paramname"><em>matrixQ</em>, </td>
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          <td></td>
          <td class="paramtype">bool&#160;</td>
          <td class="paramname"><em>computeU</em>&#160;</td>
        </tr>
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          <td></td>
          <td>)</td>
          <td></td><td></td>
        </tr>
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<p>Computes Schur decomposition of a Hessenberg matrix H = Z T Z^T. </p>
<dl class="params"><dt>Parameters</dt><dd>
  <table class="params">
    <tr><td class="paramdir">[in]</td><td class="paramname">matrixH</td><td><a class="el" href="classEigen_1_1Matrix.html" title="The matrix class, also used for vectors and row-vectors.">Matrix</a> in Hessenberg form H </td></tr>
    <tr><td class="paramdir">[in]</td><td class="paramname">matrixQ</td><td>orthogonal matrix Q that transform a matrix A to H : A = Q H Q^T </td></tr>
    <tr><td class="paramdir"></td><td class="paramname">computeU</td><td>Computes the matriX U of the Schur vectors </td></tr>
  </table>
  </dd>
</dl>
<dl class="section return"><dt>Returns</dt><dd>Reference to <code>*this</code> </dd></dl>
<p>This routine assumes that the matrix is already reduced in Hessenberg form matrixH using either the class <a class="el" href="classEigen_1_1HessenbergDecomposition.html" title="Reduces a square matrix to Hessenberg form by an orthogonal similarity transformation.">HessenbergDecomposition</a> or another mean. It computes the upper quasi-triangular matrix T of the Schur decomposition of H When computeU is true, this routine computes the matrix U such that A = U T U^T = (QZ) T (QZ)^T = Q H Q^T where A is the initial matrix</p>
<p>NOTE Q is referenced if computeU is true; so, if the initial orthogonal matrix is not available, the user should give an identity matrix (Q.setIdentity())</p>
<dl class="section see"><dt>See also</dt><dd>compute(const MatrixType&amp;, bool) </dd></dl>

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<h2 class="memtitle"><span class="permalink"><a href="#a2d89e0ee94baa7ebe226e68134cc36a2">&#9670;&nbsp;</a></span>info()</h2>

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          <td class="memname"><a class="el" href="group__enums.html#ga85fad7b87587764e5cf6b513a9e0ee5e">ComputationInfo</a> <a class="el" href="classEigen_1_1RealSchur.html">Eigen::RealSchur</a>&lt; MatrixType_ &gt;::info </td>
          <td>(</td>
          <td class="paramname"></td><td>)</td>
          <td> const</td>
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<p>Reports whether previous computation was successful. </p>
<dl class="section return"><dt>Returns</dt><dd><code>Success</code> if computation was successful, <code>NoConvergence</code> otherwise. </dd></dl>

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<h2 class="memtitle"><span class="permalink"><a href="#a9f939aaf24a1fa73e9f69f7566500e69">&#9670;&nbsp;</a></span>matrixT()</h2>

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template&lt;typename MatrixType_ &gt; </div>
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          <td class="memname">const MatrixType&amp; <a class="el" href="classEigen_1_1RealSchur.html">Eigen::RealSchur</a>&lt; MatrixType_ &gt;::matrixT </td>
          <td>(</td>
          <td class="paramname"></td><td>)</td>
          <td> const</td>
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<p>Returns the quasi-triangular matrix in the Schur decomposition. </p>
<dl class="section return"><dt>Returns</dt><dd>A const reference to the matrix T.</dd></dl>
<dl class="section pre"><dt>Precondition</dt><dd>Either the constructor RealSchur(const MatrixType&amp;, bool) or the member function compute(const MatrixType&amp;, bool) has been called before to compute the Schur decomposition of a matrix.</dd></dl>
<dl class="section see"><dt>See also</dt><dd>RealSchur(const MatrixType&amp;, bool) for an example </dd></dl>

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<h2 class="memtitle"><span class="permalink"><a href="#a1c9ed0b7109f58621557005c59ea6f99">&#9670;&nbsp;</a></span>matrixU()</h2>

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          <td>(</td>
          <td class="paramname"></td><td>)</td>
          <td> const</td>
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<p>Returns the orthogonal matrix in the Schur decomposition. </p>
<dl class="section return"><dt>Returns</dt><dd>A const reference to the matrix U.</dd></dl>
<dl class="section pre"><dt>Precondition</dt><dd>Either the constructor RealSchur(const MatrixType&amp;, bool) or the member function compute(const MatrixType&amp;, bool) has been called before to compute the Schur decomposition of a matrix, and <code>computeU</code> was set to true (the default value).</dd></dl>
<dl class="section see"><dt>See also</dt><dd>RealSchur(const MatrixType&amp;, bool) for an example </dd></dl>

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<h2 class="memtitle"><span class="permalink"><a href="#a10f9307a8dc2259c86e6dba0edbde308">&#9670;&nbsp;</a></span>setMaxIterations()</h2>

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          <td>(</td>
          <td class="paramtype"><a class="el" href="classEigen_1_1RealSchur.html#ad3a6ac65243d901525158f418c4d0582">Index</a>&#160;</td>
          <td class="paramname"><em>maxIters</em></td><td>)</td>
          <td></td>
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<p>Sets the maximum number of iterations allowed. </p>
<p>If not specified by the user, the maximum number of iterations is m_maxIterationsPerRow times the size of the matrix. </p>

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<h2 class="groupheader">Member Data Documentation</h2>
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<h2 class="memtitle"><span class="permalink"><a href="#a96deb686155894864c9e5539c732b194">&#9670;&nbsp;</a></span>m_maxIterationsPerRow</h2>

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<p>Maximum number of iterations per row. </p>
<p>If not otherwise specified, the maximum number of iterations is this number times the size of the matrix. It is currently set to 40. </p>

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<hr/>The documentation for this class was generated from the following file:<ul>
<li><a class="el" href="RealSchur_8h_source.html">RealSchur.h</a></li>
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